Tiling classification variables and sub-variables with examples
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Biologists and designers have long been fascinated by repeating patterns in nature, from spirals in shells to honeycombs in bees’ nests. However, they have paid the most attention to patterns called ‘cellular foams’ seen in bone or wood, where thin walls enclose many small chambers. These structures are strong and light and usually quite rigid.
This said, many organisms build their bodies from solid pieces separated by softer joints, like a natural suit of tiles, such that these tilings can shift and often repair themselves piece by piece — yet researchers have studied them in only a few well-known cases, including fish scales and reptile armor.
If a new study, published in PNAS Nexus by researchers in Germany, is to be believed, the prevalence of tilings in nature is surprisingly more widespread.
At the outset, the researchers developed a biological definition of tiling that differed from the strict mathematical concept. This was needed because, in nature, the tiles are almost never perfectly edge to edge: there’s usually a thin, softer joint in between. The team thus defined biological tiling as a repeated arrangement of solid tiles separated by a joint material — then built a database around this idea.
They collected information of more than 120 examples from across the tree of life from published research papers, images, and expert inputs, then shortlisted 100 clear cases that fit their definition. For each example, they noted down about 70 parameters — including what the tiles and joints were made of (mineral, protein, sugar, etc.), the shape of the tiles, how the tiles touched or overlapped, their size and packing density, and the overall pattern. Finally, they used multivariate analysis to look for patterns among these traits.
To their pleasant surprise, the researchers found that architectures were far more common and diverse than expected. The examples spanned viruses, plants, arthropods, molluscs, and deuterostomes (such as echinoderms and vertebrates). Their tiles spanned a wide range in size — from nanometre-scale virus capsids to turtle shell plates tens of centimetres across.
Across this range, some motifs also recurred. Many tilings used mineral-protein or sugar-protein combinations in tiles and joints and were built from simple tile shapes arranged in a regular grid-like pattern. Many fine tilings with medium-sized tiles provided shielding and structural support at the same time.
The analyses also revealed strong preferences for certain materials. While the protostomes often combined sugar and protein, deuterostomes used minerals and protein, and plants went for sugars plus other polymers such as lignin. The overlapping tiles of the sort familiar from fish and reptile scales turned out to be especially characteristic of deuterostomes.
Next, plant tilings were found to cluster tightly because they shared sugar-based tiles and lignin joints whereas arthropod tilings were more spread out, reflecting their wide variety of forms and functions. At the same time, the researchers also found that some seemingly unrelated structures were actually quite similar on a deeper level. In particular the overlapping plates of bony fish, brittle stars, and shark teeth appeared to be similar solutions that these disparate life forms had evolved to solve similar mechanical problems, including protection and flexibility.
The researchers’ catalogue thus exposed likely evolutionary constraints but also new open questions. For instance, why do tiles in such different organisms tend to share a similar upper size limit? How do material choices control which patterns are possible? And under what ecological pressures did the common regular tiling patterns arise? According to the team’s paper, there are also other gaps that prior research hasn’t covered fully: joint materials are often poorly described and there could be many undiscovered nanoscale tilings once imaging tools catch up.
The researchers also said their database and a website they set up together form a “morphospace” that designers, engineers, and architects could browse as a library of natural design ideas. The website is accessible here: https://tessellated-materials.mpikg.mpg.de/
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Published – November 19, 2025 01:51 pm IST
